Solve for $p$, $ -\dfrac{6}{2p + 5} = -\dfrac{p + 2}{8p + 20} + \dfrac{1}{2p + 5} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $2p + 5$ $8p + 20$ and $2p + 5$ The common denominator is $8p + 20$ To get $8p + 20$ in the denominator of the first term, multiply it by $\frac{4}{4}$ $ -\dfrac{6}{2p + 5} \times \dfrac{4}{4} = -\dfrac{24}{8p + 20} $ The denominator of the second term is already $8p + 20$ , so we don't need to change it. To get $8p + 20$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ \dfrac{1}{2p + 5} \times \dfrac{4}{4} = \dfrac{4}{8p + 20} $ This give us: $ -\dfrac{24}{8p + 20} = -\dfrac{p + 2}{8p + 20} + \dfrac{4}{8p + 20} $ If we multiply both sides of the equation by $8p + 20$ , we get: $ -24 = -p - 2 + 4$ $ -24 = -p + 2$ $ -26 = -p $ $ p = 26$